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REY [17]
3 years ago
11

What is the unit rate of students to teachers as a fraction

Mathematics
2 answers:
Sholpan [36]3 years ago
6 0
1/15 or 1 over 15 would be the simplified fraction of teachers to students. In other words, there are 15 students per 1 teacher.
aev [14]3 years ago
4 0
1 teacher per 15 students
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For an arithmetic sequence, a35=57. If the common difference is 5. Find a1 and the sum of the first 61 terms.
Flauer [41]

 

\displaystyle\bf\\a_{35}=57\\r=5\\----\\a_1=?\\S_{61}=?\\----\\Solve:\\1)\\a_1=a_{35}-(35-1)\times r=57-34\times 5=57-170=-113\\\boxed{\bf a_1=-113}\\\\

.

\displaystyle\bf\\2)\\A_{61}=a_1+(61-1)\times r=-113+60\times5=-113+300=187\\\\S_{61}=(-113)+(-108)+(-103)+...+(-8)+(-3)+2+7+12+...+187\\\\S_{61}=SA+SB\\\\SA=(-113)+(-108)+(-103)+...+(-8)+(-3)=-(3+8+103+108+113)\\\\n=\frac{113-8}{5}+1=\frac{105}{5}+1=21+1=22~terms\\SA=-\Big( \frac{n(113+3)}{2} \Big)=-\Big( \frac{22\times116}{2} \Big)=-11\times116 =-1276

.

\displaystyle\bf\\SB=2+7+12+...+187\\\\n=\frac{187-2}{5}+1=\frac{185}{5}+1=37+1=38~terms\\\\SB=\frac{n(187+2)}{2}=\frac{38\times189}{2}=19\times189=3591\\\\S_{61}=SA+SB=-1276+3591=2315\\\\\boxed{\bf S_{61}=2315}    

 

 

8 0
2 years ago
A hot air balloon went from an elevation of 4,064 feet to an elevation of 3,322 feet in 28 minutes. What
ELEN [110]

Answer:

<em>The air balloon descends 26.5 feet per minute</em>

Step-by-step explanation:

<u>Rate of Change</u>

The rate of change is a measure that compares two quantities, usually to know how one variable changes in time.

The hot air balloon was 4,064 feet high and, 28 minutes later, it went to 3,322 feet. We can calculate the rate of descent R by dividing the change of elevation over time:

\displaystyle R=\frac{3,322-4,064}{28}=\frac{-742}{28}=-26.5

Thus the air balloon descends 26.5 feet per minute

3 0
3 years ago
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
Vladimir79 [104]

Answer:

a. T² - T¹ = d ( A. P) -5

b. T²/T¹ = r (G. P) 3/4

Step-by-step explanation:

a. 15 - 20 = -5

b. 15/20 = 3/4

4 0
2 years ago
Ron made 3 pitchers of lemonade to sell at a lemonade stand. The cost of making the lemonade is 50 cents per pitcher of lemonade
julia-pushkina [17]

Answer:

3.90 I think.

Step-by-step explanation:

first, 15×36. then subtract 50 three times.

6 0
2 years ago
Read 2 more answers
Explain in easy terms, how the signs of the last terms of the two binomial factors of a trinomial are determined?
shutvik [7]

Explanation:

It helps to understand the process of multiplying the binomials. Consider the simple case ...

  (x +a)(x +b)

The product is ...

  (x +a)(x +b) = x² +(a+b)x + ab

If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.

If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).

___

Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.

<u>Example</u>:

  x² -x -6

 -6 tells you the factors will have different signs. -x tells you the one with the largest magnitude will be negative.

  -6 = -6×1 = -3×2 = ... (other factor pairs have a negative factor with a smaller magnitude)

 The sums of these factor pairs are -5 and -1. We want the factor pair that has a sum of -1, the coefficient of x in the trinomial.

  x² -x -6 = (x -3)(x +2)

5 0
3 years ago
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